We present a brief survey on the compression of discrete measures by Caratheodory-Tchakaloff Subsampling, its implementation by Linear or Quadratic Programming and the application to multivariate polynomial Least Squares. We also give an algorithm that computes the corresponding CaratheodoryTchakaloff (CATCH) points and weights for polynomial spaces on compact sets and manifolds in 2D and 3D. 2...

A short proof of the Caratheodory conjecture about index of an isolated umbilic on the convex 2–dimensional sphere is suggested.

This paper studies the existence and uniqueness of a mild solution, satisfying Caratheodory conditions, for a neutral stochastic partial functional differential equation with infinite delays and Poisson jumps.

In this paper, we study the existence and regularity of positive solution for an elliptic system on a bounded and regular domain. The non linearities in this equation are functions of Caratheodory type satisfying some exponential growth conditions.

In the present work we obtain existence results for Hammerstein type integro-differential inclusions in a finite dimensional space for the cases when the integral multifunction satisfies upper Caratheodory conditions and when it is almost lower semicontinuous.

Starting with a σ-finite measure on an algebra, we define a pseudometric and show how measurable sets from the Caratheodory Extension Theorem can be thought of as limit points of Cauchy sequences in the algebra.

Helly?s, Radon?s, and Caratheodory?s theorems are the basic of convex analysis have an important place. These been studied by different authors for classes convexity. theorem B-1 - sets has proved before Adilov Ye?ilce. In this article, Helly?s Radon?s discussed examined these sets.

A functional equation in dynamic programming is developed using multistage allocation processs. The existence of the solution of this equation is proved using caratheodory successive approximation process. Uniqueness of the solution is established.